How-to use あるいは to link alternative possibilities
The grammar pattern あるいは is used to link two or more alternatives to the point wherein both (or all) alternatives are possible all at the same time. Given that, context usually implies that there is in fact a best choice amongst all the possibilities. The actual translation for the phrasing あるいは is one that also particularly depends on the context in which it is being used, with the most common translations being simply “or,” and “either X or Y.” In other contexts, it can be more naturally worded as “possibly, alternatively, perhaps, in some cases, etc.” The kanji for あるい is 或(い), which translates to “some, one, or, possibly, a certain, etc.” This is the same ある we use when we say あるNOUN to mean “a certain NOUN,” “some NOUN,” etc. However, as is with that example, the ある in あるいは almost always appears in kana form. Additionally, あるいは is mostly used in formal speech or written language.
あるいは + NOUN
あるいは + CLAUSE
Suiyoubi wa doudesu ka? Arui wa kinyoubi desuga.
How does Wednesday sound? Another possibility would be Friday.
Sanji gogo made ni office ni shukudai (w)o dashite kudasai. Arui wa net de dashite kudasai.
“Please turn in your assignment to my office by 3 P.M. Or, you can submit it online.”
Kare wa nete imashita. Aruiwa nete ita furi (w)o shite imashita.
“He was asleep. Or perhaps he was just pretending to be asleep.”
Tokodoki ni erabareta outachi wa
“Every so often, a new king is chosen.”
Arui wa ikite chikara (w)o furui
“Some lived to exercise their power.”
Arui wa shi to tomo ni sari
“Others chose to pass on in death without leaving a mark.”
Mata arui wa sorera (w)o mimamoritsuduketa
“And then there were those who chose to continually watch over their subjects.”
*Example from episode 1 of K: Return of Kings
Saa, kore de kimi wa himitsu (w)o mamorazaru (w)o enai tachiba ni natta wa. Kono ken ni kanshite kuchi (w)o tsugumuka, arui wa…
“Now then, with this, it looks like you’re obligated to keep this a secret between us. I trust you’ll keep quiet about this matter? Otherwise…”
*Example from episode 5 of Rewrite